O2 + CH4 = H2O + CO2 + C

O_2 oxygen + CH_4 methane ⟶ H_2O water + CO_2 carbon dioxide + C activated charcoal

Balance the chemical equation algebraically: O_2 + CH_4 ⟶ H_2O + CO_2 + C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 CH_4 ⟶ c_3 H_2O + c_4 CO_2 + c_5 C Set the number of atoms in the reactants equal to the number of atoms in the products for O, C and H: O: | 2 c_1 = c_3 + 2 c_4 C: | c_2 = c_4 + c_5 H: | 4 c_2 = 2 c_3 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1 - 1 c_3 = 2 c_1 - 2 c_4 = 1 c_5 = c_1 - 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 4 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 2 CH_4 ⟶ 4 H_2O + CO_2 + C

+ ⟶ + +

oxygen + methane ⟶ water + carbon dioxide + activated charcoal

Construct the equilibrium constant, K, expression for: O_2 + CH_4 ⟶ H_2O + CO_2 + C Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 3 O_2 + 2 CH_4 ⟶ 4 H_2O + CO_2 + C Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i O_2 | 3 | -3 CH_4 | 2 | -2 H_2O | 4 | 4 CO_2 | 1 | 1 C | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 3 | -3 | ([O2])^(-3) CH_4 | 2 | -2 | ([CH4])^(-2) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 1 | 1 | [CO2] C | 1 | 1 | [C] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([O2])^(-3) ([CH4])^(-2) ([H2O])^4 [CO2] [C] = (([H2O])^4 [CO2] [C])/(([O2])^3 ([CH4])^2)

Construct the rate of reaction expression for: O_2 + CH_4 ⟶ H_2O + CO_2 + C Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 3 O_2 + 2 CH_4 ⟶ 4 H_2O + CO_2 + C Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i O_2 | 3 | -3 CH_4 | 2 | -2 H_2O | 4 | 4 CO_2 | 1 | 1 C | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) CH_4 | 2 | -2 | -1/2 (Δ[CH4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) C | 1 | 1 | (Δ[C])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/3 (Δ[O2])/(Δt) = -1/2 (Δ[CH4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | methane | water | carbon dioxide | activated charcoal formula | O_2 | CH_4 | H_2O | CO_2 | C name | oxygen | methane | water | carbon dioxide | activated charcoal IUPAC name | molecular oxygen | methane | water | carbon dioxide | carbon